# Should I delete the question that is similar to the others asked before?

For example, I asked this Is $\{(x,y)|y=\sin(\frac{1}{x})\}\cup(0,1)$ connected on $R^2$?, in the answer someone points out that a similar question was asked and discussed before. The title looks different so I cannot find it by searching, should I delete questions like this myself( If reputation lost is a consideration, should I delete it before any answer is upvote?)?

No, you shouldn't. Duplicates are generally useful (there are exceptional cases such as the 27th duplicate of $0.999999...=1$).
What you could do (once you became aware of duplication) was to flag your question for closure: flag $\to$ it is a duplicate. Does not matter now because there is already a vote to close.